Answer: The 95% confidence interval for the mean of x is (94.08, 101.92) .
Step-by-step explanation:
We are given that ,
A random variable x has a Normal distribution with an unknown mean and a standard deviation of 12.
i.e. ![\sigma= 12](https://tex.z-dn.net/?f=%5Csigma%3D%2012)
Also, it is given that , Sample mean
having sample size : n= 36
For 95% confidence ,
Significance level : ![\alpha=1-0.95=0.05](https://tex.z-dn.net/?f=%5Calpha%3D1-0.95%3D0.05)
By using the z-value table , the two-tailed critical value for 95% Confidence interval :
![z_{\alpha/2}=z_{0.025}=1.96](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3Dz_%7B0.025%7D%3D1.96)
We know that the confidence interval for unknown population mean
is given by :-
![\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%5Cpm%20z_%7B%5Calpha%2F2%7D%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
, where
= Sample mean
= Population standard deviation
= Critical z-value.
Substitute all the given values, then the required confidence interval will be :
![98\pm (1.96)\dfrac{12}{\sqrt{36}}](https://tex.z-dn.net/?f=98%5Cpm%20%281.96%29%5Cdfrac%7B12%7D%7B%5Csqrt%7B36%7D%7D)
![=98\pm (1.96)\dfrac{12}{6}](https://tex.z-dn.net/?f=%3D98%5Cpm%20%281.96%29%5Cdfrac%7B12%7D%7B6%7D)
![=98\pm (1.96)(2)](https://tex.z-dn.net/?f=%3D98%5Cpm%20%281.96%29%282%29)
![=98\pm 3.92=(98-3.92,\ 98+3.92)\\\\=( 94.08,\ 101.92)](https://tex.z-dn.net/?f=%3D98%5Cpm%203.92%3D%2898-3.92%2C%5C%2098%2B3.92%29%5C%5C%5C%5C%3D%28%0994.08%2C%5C%20101.92%29)
Therefore, the 95% confidence interval for the mean of x is (94.08, 101.92) .
Answer:
is 1/1 a option? like one over one, as in a fraction....?
Step-by-step explanation:
Unless you just want to give money to the ice cream truck, for 0 items, you will pay 0.
Since the price of each item is $0.77, for one item you will pay $0.77. (Is that a surprise?)
Then for two items, you will pay $0.77 for each one, or $0.77 + 0.77 = $1.54. You can also compute this by making use of the fact that multiplication is a shortcut for repeated addition. The price can be found by $0.77×2 = $1.54 = f(2).
Similarly, for 3 items, you can add $0.77 three times: $0.77 + 0.77 + 0.77 = f(3), or you can use multiplication: $0.77×3 = $2.31 = f(3).
a) Our table looks like
(x, f(x))
(0, 0)
(1, 0.77)
(2, 1.54)
(3, 2.31)
b) By now, I'm sure you have realized that to find the price of x items, you multiply 0.77 by x.
f(x) = 0.77x
Answer:
y = -1
Step-by-step explanation:
1/2 of 4y + (y + 3) = 0
1/2 X 4y + (y + 3) = 0
4y/2 + (y + 3) = 2y + y + 3 = 0
3y = -3
∴ y = -1